TY - JOUR
T1 - A Penalty Function Method for Constrained Molecular Dynamics Simulation
AU - Gunaratne , A.
AU - Wu , Z.
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 496
EP - 517
PY - 2011
DA - 2011/08
SN - 8
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/698.html
KW - Constrained molecular dynamics, Verlet algorithm, Shake algorithm, Lagrange multipliers method, penalty function method.
AB - <p style="text-align: justify;">We propose a penalty-function method for constrained molecular
dynamics simulation by defining a quadratic penalty function for the constraints.
The simulation with such a method can be done by using a conventional,
unconstrained solver only with the penalty parameter increased in an
appropriate manner as the simulation proceeds. More specifically, we scale the
constraints with their force constants when forming the penalty terms. The
resulting force function can then be viewed as a smooth continuation of the
original force field as the penalty parameter increases. The penalty function
method is easy to implement and costs less than a Lagrange multiplier method,
which requires the solution of a nonlinear system of equations in every time
step. We have first implemented a penalty function method in CHARMM and
applied it to protein Bovine Pancreatic Trypsin Inhibitor (BPTI). We compared
the simulation results with Verlet and Shake, and found that the penalty
function method had high correlations with Shake and outperformed Verlet.
In particular, the RMSD fluctuations of backbone and non-backbone atoms
and the velocity auto correlations of $C_{\alpha}$ atoms of the protein calculated by
the penalty function method agreed well with those by Shake. We have also
tested the method on a group of argon clusters constrained with a set of interatomic
distances in their global energy minimum states. The results showed
that the method was able to impose the constraints effectively and the clusters
tended to converge to their energy minima more rapidly than not confined by
the constraints.</p>